Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation

TL;DR

This paper introduces a novel disentanglement approach combining field theory and stochastic simulation to analyze ground states of quantum spin systems, providing both analytical expansions and numerical importance sampling methods.

Contribution

It develops an analytical and numerical framework using the disentanglement approach for studying quantum spin ground states, integrating field theory and stochastic simulation techniques.

Findings

Analytical expansion of ground state expectation values using saddle point approximation.

Numerical computation of observables via importance sampling based on saddle point configurations.

Application of methods to quantum Ising models in 1, 2, and 3 dimensions.

Abstract

We develop an analytical and numerical framework based on the disentanglement approach to study the ground states of many-body quantum spins systems. In this approach, observables are expressed as functional integrals over scalar fields, where the relevant measure is the Wiener measure. We identify the leading contribution to these integrals, given by the saddle point field configuration. Analytically, this can be used to develop an exact field-theoretical expansion of the functional integrals, performed by means of appropriate Feynman rules. The expansion can be truncated to the desired order to obtain approximate analytical results for ground state expectation values. Numerically, the saddle point configuration can be used to compute physical observables by means of an exact importance sampling scheme. We illustrate our methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions. Our analytical and numerical results are applicable to a broad class of many-body quantum spin systems, bridging concepts from quantum lattice models, continuum field theory, and classical stochastic processes.